{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OW7P7T45CGG3WFCQ2X2U55LPLM","short_pith_number":"pith:OW7P7T45","canonical_record":{"source":{"id":"1007.3500","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-07-20T20:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"edb93f10c467dd0a01287f9a05f3ae35a87c6f4f10f61e1cbb5ed9e1c3eac3a3","abstract_canon_sha256":"27f9e7788d157cd57b2205a9484543fd726d018c946ada1307ffbea63bee43db"},"schema_version":"1.0"},"canonical_sha256":"75beffcf9d118dbb1450d5f54ef56f5b1fddc72040dfa00177fa8a6f96813bc3","source":{"kind":"arxiv","id":"1007.3500","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3500","created_at":"2026-05-18T02:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3500v2","created_at":"2026-05-18T02:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3500","created_at":"2026-05-18T02:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"OW7P7T45CGG3","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OW7P7T45CGG3WFCQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OW7P7T45","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OW7P7T45CGG3WFCQ2X2U55LPLM","target":"record","payload":{"canonical_record":{"source":{"id":"1007.3500","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-07-20T20:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"edb93f10c467dd0a01287f9a05f3ae35a87c6f4f10f61e1cbb5ed9e1c3eac3a3","abstract_canon_sha256":"27f9e7788d157cd57b2205a9484543fd726d018c946ada1307ffbea63bee43db"},"schema_version":"1.0"},"canonical_sha256":"75beffcf9d118dbb1450d5f54ef56f5b1fddc72040dfa00177fa8a6f96813bc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:06:12.277216Z","signature_b64":"Z/H2x8PH6qMZRSoXUWp/jnFz9jwBt35zR2zWaHrUIrJGtAO9gQpQKtLMTdKaPiFM4sDZrrkbm3q4AYPKsnJWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75beffcf9d118dbb1450d5f54ef56f5b1fddc72040dfa00177fa8a6f96813bc3","last_reissued_at":"2026-05-18T02:06:12.276288Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:06:12.276288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.3500","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K4K6FHJ8CHso3aA1ZnEWMhXYLXS/muIoe3Orz3rHDlhQf7wg5zA4zU4G6ZKdm0ZiRX616zQ5mHWZAG7k/5AbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:42:08.591713Z"},"content_sha256":"6fa2b9f43cb5e88fb5ea333243b6fddbce55c70bfbf972136fc523f929389c29","schema_version":"1.0","event_id":"sha256:6fa2b9f43cb5e88fb5ea333243b6fddbce55c70bfbf972136fc523f929389c29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OW7P7T45CGG3WFCQ2X2U55LPLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal linear reconstruction of dark matter from halo catalogs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Gary Bernstein, Ravi K. Sheth (UPenn), Yan-Chuan Cai","submitted_at":"2010-07-20T20:00:06Z","abstract_excerpt":"We derive the weight function w(M) to apply to dark-matter halos that minimizes the stochasticity between the weighted halo distribution and its underlying mass density field. The optimal w(M) depends on the range of masses being used in the estimator. In N-body simulations, the Poisson estimator is up to 15 times noisier than the optimal. Implementation of the optimal weight yields significantly lower stochasticity than weighting halos by their mass, bias or equal. Optimal weighting could make cosmological tests based on the matter power spectrum or cross-correlations much more powerful and/o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3500","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ob+HNrKw5zegt0bM0wuxt7J8VIi0mInvjwHnD4W4p0diESuKMyxnJuotodlKoHGLjdMoBe1F7WPHjgThhr9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:42:08.592441Z"},"content_sha256":"f1982ea71e7e2ad835749f52856f58fc3d6ba3a1562a84c3f2d19a8cf071df81","schema_version":"1.0","event_id":"sha256:f1982ea71e7e2ad835749f52856f58fc3d6ba3a1562a84c3f2d19a8cf071df81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OW7P7T45CGG3WFCQ2X2U55LPLM/bundle.json","state_url":"https://pith.science/pith/OW7P7T45CGG3WFCQ2X2U55LPLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OW7P7T45CGG3WFCQ2X2U55LPLM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T19:42:08Z","links":{"resolver":"https://pith.science/pith/OW7P7T45CGG3WFCQ2X2U55LPLM","bundle":"https://pith.science/pith/OW7P7T45CGG3WFCQ2X2U55LPLM/bundle.json","state":"https://pith.science/pith/OW7P7T45CGG3WFCQ2X2U55LPLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OW7P7T45CGG3WFCQ2X2U55LPLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OW7P7T45CGG3WFCQ2X2U55LPLM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"27f9e7788d157cd57b2205a9484543fd726d018c946ada1307ffbea63bee43db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-07-20T20:00:06Z","title_canon_sha256":"edb93f10c467dd0a01287f9a05f3ae35a87c6f4f10f61e1cbb5ed9e1c3eac3a3"},"schema_version":"1.0","source":{"id":"1007.3500","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3500","created_at":"2026-05-18T02:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3500v2","created_at":"2026-05-18T02:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3500","created_at":"2026-05-18T02:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"OW7P7T45CGG3","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OW7P7T45CGG3WFCQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OW7P7T45","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:f1982ea71e7e2ad835749f52856f58fc3d6ba3a1562a84c3f2d19a8cf071df81","target":"graph","created_at":"2026-05-18T02:06:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We derive the weight function w(M) to apply to dark-matter halos that minimizes the stochasticity between the weighted halo distribution and its underlying mass density field. The optimal w(M) depends on the range of masses being used in the estimator. In N-body simulations, the Poisson estimator is up to 15 times noisier than the optimal. Implementation of the optimal weight yields significantly lower stochasticity than weighting halos by their mass, bias or equal. Optimal weighting could make cosmological tests based on the matter power spectrum or cross-correlations much more powerful and/o","authors_text":"Gary Bernstein, Ravi K. Sheth (UPenn), Yan-Chuan Cai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-07-20T20:00:06Z","title":"Optimal linear reconstruction of dark matter from halo catalogs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3500","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6fa2b9f43cb5e88fb5ea333243b6fddbce55c70bfbf972136fc523f929389c29","target":"record","created_at":"2026-05-18T02:06:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"27f9e7788d157cd57b2205a9484543fd726d018c946ada1307ffbea63bee43db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-07-20T20:00:06Z","title_canon_sha256":"edb93f10c467dd0a01287f9a05f3ae35a87c6f4f10f61e1cbb5ed9e1c3eac3a3"},"schema_version":"1.0","source":{"id":"1007.3500","kind":"arxiv","version":2}},"canonical_sha256":"75beffcf9d118dbb1450d5f54ef56f5b1fddc72040dfa00177fa8a6f96813bc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75beffcf9d118dbb1450d5f54ef56f5b1fddc72040dfa00177fa8a6f96813bc3","first_computed_at":"2026-05-18T02:06:12.276288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:12.276288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z/H2x8PH6qMZRSoXUWp/jnFz9jwBt35zR2zWaHrUIrJGtAO9gQpQKtLMTdKaPiFM4sDZrrkbm3q4AYPKsnJWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:12.277216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3500","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fa2b9f43cb5e88fb5ea333243b6fddbce55c70bfbf972136fc523f929389c29","sha256:f1982ea71e7e2ad835749f52856f58fc3d6ba3a1562a84c3f2d19a8cf071df81"],"state_sha256":"b824b192b1ff10900a89851ddbda944b003954145097ec04c1510f4a054e6920"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjaz5aRZYohev6iU0DW2HPilGn2vM47M0u8uV6q9UN00fw77rkJqJo0KHu++BsAjubM4UQCuds8unpwX5Dn/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:42:08.596422Z","bundle_sha256":"c39c796a56d772d044988aa0253f46cb572958e454670e27079ae007cae1e7ea"}}